On asymptotic analysis of quasi-regenerative processes

In queuing theory and related fields, many methods of asymptotic analysis of the behaviour of stochastic processes are based on the analysis of regenerative processes. However, the behaviour of some complex technical systems cannot be described by regenerative processes. For example, the behaviour of one part of some system affects the behaviour of another part of this system, and vice versa. In this case, the total process of behaviour of both subsystems is not regenerative. However, in many technical systems, these non-regenerative processes are close ``in some sense'' to regenerative processes. Hence, its asymptotic behaviour can be studied.